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Monotonic stable solutions for minimum coloring games

Hamers,H.J.M.
; 
Miquel,S.
; 
Norde,H.W.
Abstract
For the class of minimum coloring games (introduced by Deng et al. Math Oper Res, 24:751ā€“766, 1999) we investigate the existence of population monotonic allocation schemes (introduced by Sprumont Games Econ Behav 2:378ā€“394, 1990). We show that a minimum coloring game on a graph G has a population monotonic allocation scheme if and only if G is (P4,2K2) -free (or, equivalently, if its complement graph Gā€¾ is quasi-threshold). Moreover, we provide a procedure that for these graphs always selects an integer population monotonic allocation scheme.
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2014-06-01
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Tilburg University Research Output Collection
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Hamers, H J M, Miquel, S & Norde, H W 2014, 'Monotonic stable solutions for minimum coloring games', Mathematical Programming, vol. 145, no. 1-2, pp. 509-529. https://doi.org/10.1007/s10107-013-0655-y
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https://hdl.handle.net/20.500.14602/59171
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